The k-generalized Fibonacci sequence $F^{\left(k\right)}:=(F_n^{\left(k\right)}{)}_{n\ge -(k-2)}$ is the linear recurrent sequence of order k, whose first k terms are $0,\dots ,0,1$ and each term afterwards is the sum of the preceding k terms. In this paper, we extend $F^{\left(k\right)}$ to negative indices and give an upper bound on the absolute value of its largest zero in terms of k. In particular, we find that the zero-multiplicity of the k-generalized Fibonacci sequence is exactly $k(k-1)/2$ for all $k\in [4,500]$. We prove that the zero multiplicity of the k-generalized Fibonacci sequence is at least $k(k-1)/2$ for all $k\ge 2$.

所述ķ -generalized斐波纳契数列$F^{（ķ）}：=（F_{ñ}^{（ķ）}{）}_{ñ\ge -（ķ-2）}$是阶k的线性递归序列，其前k个项是$0，\dots ，0，\mathrm{1个}$之后的每个项是前k个项的总和。在本文中，我们扩展$F^{（ķ）}$到负指数，并以k为单位给出其最大零的绝对值的上限。特别是，我们发现k广义斐波那契数列的零重数正好是$ķ（ķ-\mathrm{1个}）/2$ 对全部 $ķ\in [4，500]$。我们证明了k广义斐波那契数列的零多重性至少为$ķ（ķ-\mathrm{1个}）/2$ 对全部 $ķ\ge 2$。